Job/Class mounts would be neat. Especially if they were through Job Quests (Rather than spam a ton of duties...). Even better if they were from some sort of job/class based side activity (You know, like Masked Carnivale... Only good)

Paladin: An armoured Pegasus.
Warrior: An armoured Manticore
Dark Knight: A giant armoured Raven that's formed out of the Abyss made physical (So dark red/purple and leaving a sort of inky trail behind it)

White Mage: A phoenix
Scholar: A butterfly
Astrologian: An Eagle made out of stars like a constellation.

Monk: A tiger, that gets enhanced with Chakra when it starts to fly.
Dragoon: A dragon. With Blood of the Dragon style glowy wyrms. (Reference)
Ninja: A giant spinning shuriken
Samurai: A nine-tailed Fox

Bard: IDK...
Machinist: Clockwork Dragon

Black Mage: A griffon where the eagle half is made out of fire and the lion part is made out of ice.
Summoner: Freaking Bahamut wings.
Red Mage: IDK...
Blue Mage: A Morbol